In this paper, we describe student understanding of the "force concept" (basic concepts of Newtonian mechanics) by representing it as a vector-valued quantity, which we refer to as the "score-state vector," in a (30-dimensional) Force Concept Inventory (FCI) score space. We use a large ensemble of FCI results collected…

Over the past half-century, numerous attempts have been made to derive the centripetal acceleration formula by treating circular motion as a superposition of uniform and accelerated rectilinear motions over short time intervals. Critical examination reveals that these methods are manifestations of the same approach pioneered by Huygens to…

A Slinky is a loose helical coil spring and is a well-known educational toy. In this paper a model for a Slinky is presented. The Slinky is represented as a sequence of rigid half coils connected by torsional springs. A range of Slinky configurations in static equilibrium are calculated. Where possible the torsion spring model is compared with the…

The study of coordination complexes in general and inorganic chemistry courses is facilitated by theoretical frameworks such as crystal field theory (CFT) and ligand field theory (LFT). The angular overlap model (AOM) is alternative approach that quantifies metal-ligand interactions based on the geometric configuration of a given complex. In this…

On 24 June 1994 at Fairchild Air Force Base, during practice for an air show, a low-flying B-52H aircraft banked its wings vertically and crashed. Emphasizing the activity of modeling drag and gravity, these notes examine the possibility of recovery with several models. First, with algebra, historical data lead to a model where in a free fall near…

Ion transport, involving the diffusion and migration of ions within the electrolyte, stands as a fundamental concept in electrochemistry and serves as the driving force for electrochemical reactions. Electric double layers are critical in the fields of electrochemical energy storage and chemical conversion, constituting a central focus of…

Quantum science is in the news daily and engages students' interest and curiosity. A fundamental quantum science concept that underpins medical imaging, quantum computing and many future technologies is quantum spin. Quantum spin can explain many physical phenomena that are in the lower secondary school curriculum, such as magnetism and light,…

In 2017, the University of Utah experienced a tragedy that accelerated already proposed changes to the physics and astronomy graduate program. This article outlines the changes made to the graduate program and discusses students' experiences with the early implementation of the new policies. In-depth, open-ended interviews were conducted with…

We discuss how research on student difficulties was used as a guide to develop, validate, and evaluate a Quantum Interactive Learning Tutorial (QuILT) to help students learn how to determine the completely symmetric bosonic or completely antisymmetric fermionic wave function and be able to compare and contrast them from the case when the particles…

To address existing challenges in teaching theoretical mechanics and enhance instructional quality, the teaching team implemented innovative reforms. Guided by a "student-centered" philosophy and powered by digital intelligence technologies with "Chaoxing" AI as the engine, the course reconstructed a three-dimensional objective…

This paper examines the technologisation of the pedagogical space "classroom". We will discuss the development and establishment of the subject-specific classroom system in the German Democratic Republic (GDR, East Germany, 1949-1989) by taking a closer look at organisational-structural conditions and responsibilities, as well as at the…

There is a growing need for college science faculty to teach a diverse group of learners. The Universal Design for Learning (UDL) framework can be used to create inclusive learning materials and activities in the higher education science classroom. A UDL Academy introduced science faculty to the UDL framework, which led to them implementing UDL in…

We present a complete, soup to nuts, modeling activity of a falling column of water. Many colleagues have used this material in teaching applications of first order separable differential equations. We describe how the material can be presented with students collecting their own data from online videos. One can then either offer the differential…

Pitching velocity is a crucial factor in effective baseball pitching performance. Upper-body-focused training is prevalent in baseball training to increase pitching velocity. However, significant pitchers, including youth league baseball players, suffer from upper body injuries due to the heavy training load of the throwing arm. This article…

Many students who enroll in a first course in linear algebra major in STEM disciplines other than mathematics. Teachers who serve such students may find it difficult to provide authentic problems from these broader areas that ignite students' interest in linear algebra. In this paper, we highlight an interdisciplinary learning activity that…